Rewrite as a simplified fraction. ${0.3\overline{57} = {?}}$
Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}1000x &= 357.5757...\\ 10x &= 3.5757...\end{align*}}$ Subtracting the two equations, we have: ${990x = 354}$ ${x = \dfrac{354}{990}} $ ${x = \dfrac{59}{165}} $